Most of this DLC is kept separate to your main island, but after unlocking these new building features you will then be able to perform them on your own home. In a Q&A session on the DLC with Nintendo reps, the company said no new furniture would be locked behind the Happy Home Paradise DLC. Eurogamer also asked specifically what would happen if you unsubscribed from Nintendo Switch Online + Expansion Pack after using it to play the expansion:
“Players can still continue to access certain things they have unlocked in Animal Crossing: New Horizons - Happy Home Paradise on their main island, including adding counters, partition walls, as well as adding ambient lighting and soundscapes, even if their access to Animal Crossing: New Horizons - Happy Home Paradise is suspended," a Nintendo spokesperson told me. "However, it will not be possible to visit the archipelago if players lose access to the DLC. To be able to visit the archipelago and take on requests of designing vacation homes again, you will need to purchase the DLC separately or renew the Nintendo Switch Online + Expansion Pack membership."